The Committee of Seventy, a good-government watchdog group, and the local chapter of the League of Women Voters have been trying to set up a debate between Williams and Alvarez for weeks.
Alvarez readily agreed. Williams stalled and then declined.
Williams yesterday questioned why he should "give this guy a platform" and noted that he is pretty busy with his job.
"I'm dealing with people who are getting shot, murdered and raped, priests who are pedophiles," Williams said. "I'm still reorganizing the system."
Williams, acknowledging how he pushed for a debate in 2005, conceded that he might give Alvarez political ammunition in the race by ducking a debate.
"It's not a perfect science," Williams said of the political gamesmanship. "It's a tough call."
Alvarez said declining a debate makes Williams look weak, with a disregard for the city's voters.
"Politics aside, strategy aside, people have a right to hear the issues," he said. "The best way to do that is during a debate."
The poorly funded Alvarez is clearly looking for a venue in which to go negative on Williams.
He called the Daily News after an initial interview yesterday, asking to add one more quote.
This is it: "Seth's math will be as fuzzy as his mustache, and his statistics as inflated as his ego, which is why we should debate."
Williams left open just a sliver of hope for a debate - the election is four weeks from today - but seems much more interested in campaign events where Alvarez won't be present.
Williams, who once considered Abraham a mentor, clashed with her in a lively 30-minute television debate in 2005.
Williams engaged in debates in a crowded 2009 Democratic primary election after Abraham decided to not seek another term.
He also debated Michael Untermeyer, his Republican opponent, before the 2009 general election.
On Twitter: @ChrisBrennanDN